Theorem:
A trader has N kg of a certain item, a part of
which he sells at x% profit and the rest at y% loss. On the
whole his loss is P%.
Then the quantity sold at x% profit is =
(
y - P
)
N Kg
x + y
and the quantity sold at y% loss is given by =
(
x + P
)
N Kg
x + y
Example :
A trader has 50 kg of rice, a part of which he sells at
14% profit and the rest at 6% loss. On the whole his
loss is 4%. What is the quantity sold at 14% profit
and that at 6% loss?
Detail Method :
Let the quantity sold at 14% profit be
x kg. Then the quantity sold at 6% loss will be (50 - x)
kg.
For a matter of convenience suppose that the price of
rice is 1 rupee per kg.
Then price of x kg rice = Rs x and price of (50 - x) kg
rice = Rs (50 - x)
Now, we have
14% profit of x + 6% loss of (50 - x)= 4% loss of 50
or, 14% of x - 6% of (50 - x) = 4% of 50
or, 14x 300 + 6x = 200
or, 20x = 100
∴ x = 5 kg
and 50 - x = 50 - 5 = 45 kg.
Therefore, the quantity sold at 14% profit = 5 kg and
the quantity sold at 6% loss = 45 kg.
Ailigation Method :
I Part
II Part
(as there is loss on
the whole)
14
(-)4
(-)6
2
18
∴ ratio of quantities sold at 14% profit and 6% loss
= 2 : 18 = 1 : 9
∴ quantity sold at 14% profit =
50
X 1 = 5 kg,
1 + 9
and sold at 6% loss = 50 - 5 = 45 kg. Note: Numbers in the third line should always be +ve. That
is why (-) 6 - (-)4 = -2 is not taken under consideration.
Quicker Method : Here you can use direct formula :
Quantity sold at 14% profit =
(
6 - 4
)
X 50 = 5 kg and
14 + 6
the quantity sold at 6% loss =
(
14 + 4
)
X 50 = 45 kg.
14 + 6
Exercise :
A trader has 40 kg of rice, a part of which he sells at 28%
profit and the rest at 12% loss. On the whole his loss is
8%. What is the quantity sold at 28% profit and that at
12% loss?
A trader has 48 kg of rice, a part of which he sells at 16%
profit and the rest at 8% loss. On the whole his loss is
6%. What is the quantity sold at 16% profit and that at
8% loss?
A trader has 44 kg of rice, a part o f which he sells at 26%
profit and the rest at 18% loss. On the whole his loss is
16%. What is the quantity sold at 26% profit and that at
18% loss?
Answers :1 = 4 kg. 36 kg, 2 = 4 kg, 44 kg, 3 = 2 kg, 42 kg